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arXiv:2002.02895 · Quantum Studies Mathematics and Foundations

From thermodynamic sufficiency to information causality

Peter Harremoës

Published Feb 24, 2020• 0 citations
arXivHTMLPDF
DOI
10.1007/s40509-020-00222-w

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Recently, the principle of nonviolation of information causality [Nature 461, 1101 (2009)] has been proposed as one of the foundational properties of nature. We explore the Hardy's nonlocality theorem for two-qubit systems, in the context of generalized probability theory, restricted by the principle of nonviolation of information causality. Applying a sufficient condition for information causality violation, we derive an upper bound on the maximum success probability of Hardy's nonlocality argument. We find that the bound achieved here is higher than that allowed by quantum mechanics but still much less than what the no-signaling condition permits. We also study the Cabello type nonlocality argument (a generalization of Hardy's argument) in this context.
We present a geometric framework that provides a pathway toward resolving quantum measurement through thermodynamic entropy mechanics within causal diamond structures. Entropy mechanics demonstrates that quantum measurement represents the conversion of coherent entropy states (accessible quantum information) into decoherent entropy states (thermodynamically inaccessible information) at precise spacetime boundaries defined by light cone intersections. The universal Quantum-Thermodynamic Entropy Partition (QTEP) ratio Scoh/|Sdecoh| ≈ 2.257 emerges from von Neumann entropy analysis and is characterized by the fundamental information processing rate γ governing all quantum-to-classical transitions without requiring additional empirical input beyond standard quantum mechanics. We add definition to fundamental information units: ebits (entanglement bits) and obits (observational bits), resolving dimensional inconsistencies between thermodynamic entropy and discrete information content. Crucially, causal diamond geometry - the intersection of future and past light cones - provides calculable spacetime boundaries where entropy conversion occurs, with the universal rate γ serving as the fundamental geodesic parameter governing all timelike paths. This architecture features holographic screens of area A(p, q) encoding information and 4-volumes V(p, q) constraining processing capacity. Entropy mechanics offers a substantive refutation of the Many Worlds Interpretation by demonstrating that quantum measurement creates definite outcomes through negentropy generation rather than reality multiplication. The single causal diamond structure provides sufficient geometric and thermodynamic resources for complete energy and information conservation. Gravity emerges as bulk manifestation of information processing optimization on holographic screens, while black holes represent extreme coherent entropy organizations. This framework provides concrete, testable predictions grounded in geometric andthermodynamic principles, with the fundamental insight that quantum measurement dynamics are intrinsically connected to spacetime structure through the universal information processing rate γ governing timelike geodesics.
This thesis reports progress in two domains, causal structures and microscopic thermodynamics, both of which are pertinent in the development of quantum technologies. The first part is dedicated to the analysis of causal structure, which encodes the relationship between observed variables, in general restricting the set of possible correlations between them. Our considerations rely on a recent entropy vector method. Based on this, we develop techniques for deriving entropic constraints to differentiate between causal structures. We provide sufficient conditions for entropy vectors to be realisable within a causal structure and derive new, improved necessary conditions in terms of so-called non-Shannon inequalities. We also report that for a family of causal structures, including the bipartite Bell scenario and the bilocal causal structure, entropy vectors are unable to distinguish between classical and quantum causes, in spite of the existence of quantum correlations that are not classically reproducible. Hence, further development is needed in order to understand cause from a quantum perspective. In the second part we explore an axiomatic framework for modelling error-tolerant processes in microscopic thermodynamics. Our axiomatisation allows for the accommodation of finite precision levels, crucial for describing experiments in the microscopic regime. It leads to the emergence of manageable quantities that give insights into the feasibility and expenditure of processes, which for adiabatic processes are shown to be smooth entropy measures. Our framework also leads to thermodynamic behaviour at the macroscopic scale, meaning that for thermodynamic equilibrium states a unique function provides necessary and sufficient conditions for state transformations, like in the traditional second law.